Temporary employment and wage gap with permanent jobs: evidence from quantile regression

Transcription

1 MPRA Munich Personal RePEc Archive Temporary employment and wage gap with permanent jobs: evidence from quantile regression Giulio Bosio Department of Economics and Business Studies, University of Milan February 2009 Online at MPRA Paper No , posted 6. July :27 UTC

2 TEMPORARY EMPLOYMENT AND WAGE GAP WITH PERMANENT JOBS: EVIDENCE FROM QUANTILE REGRESSION Giulio Bosio Department of Economics and Business Studies University of Milan Abstract Previous research on wage penalty for temporary workers has focused on the conditional mean model. This paper uses micro data from the 2006 wave of the Survey of Italian Households Income and Wealth (SHIW) to examine the wage gap between temporary and permanent workers across the whole wage distribution. I apply a quantile regression models to understand whether there are glass ceiling or sticky floor for fixed-term workers and to test the hypothesis of polarization of wage profile by contract status. I also exploit a counterfactual decomposition analysis to investigate whether the gap is attributed to differences in characteristics or to differences in coefficients effect. A possible source of misspecification may arise, the endogenous selection in temporary status. In order to address the selectivity bias, I adopt an IV specification and a variant of the traditional Heckman (1978) dummy endogenous variable for the quantile framework. The main finding is a sticky floor effect, in the sense that the wage penalty for temporary workers is wider at the bottom of earnings distribution and in particular the decomposition method shows how the coefficients effect is decreasing in the upper half of wage profile. The analysis by educational level and by sector confirms the sticky floor effect. Finally correcting for endogenous self-selection in temporary contract slightly modifies the magnitude of wage gap, without changing the main patterns evidenced in the standard quantile regression. Keyword: temporary employment, quantile regression, wage gap decomposition, endogenous selection 1

3 Introduction During the last decades, European countries witnessed a significant expansion of temporary employment. The growth of fixed-term contracts has been triggered by the process of liberalization which has contributed to lessen the rigid employment protection legislation and to make more flexible the labour market. The increase of atypical contracts has generated a concern over its effects on labour market equilibrium. In particular the relative situation of temporary workers has played a central role in the numerous studies carried out in the last years on fixed-term jobs and their consequence in term of wages and employment transition. Furthermore fixed-term contracts expire automatically at the end of the term fixed without any firing cost for the employer and this means that temporary workers suffer a higher risk of unemployment and of income loss. According to the theory of compensating differentials, different working conditions in presence of the same level of competence should correspond to a wage premium for temporary workers to offset the disadvantages. However the empirical evidence shows a wage penalty for temporary jobs and in recent years several studies have investigated on this topic, finding negative earnings differentials for atypical jobs. This paper aims to investigate the differences between the wage structures of temporary and permanent workers in the Italian labour market. In particular the focus is to analyze the wage gaps across the whole pay distribution to understand whether there are glass ceilings and sticky floors for fixed-term workers in Italy. The pay gap may be different in the upper and lower tails of earnings distribution. The glass ceiling effect refers to a wider wage gap at the top of distribution, suggesting that temporary in the high-income jobs are paid less than their permanent counterparts. In contrast a sticky floor effect refers to an opposite situation, when the gap widens at the bottom of the wage distribution. I hypothesize a sort of polarization of wage profile by contract status, distinguishing between temporary and stable job, and I try to emphasize the extent to which work duration affects the location and shape of the conditional wage distribution. A growing number of studies has attempted to analyze the phenomenon and promoted greater understanding of its evolution. I evaluate the presence of a wage penalty for temporary contracts in Italy and whether the wage gap between two groups of workers is due to the distribution of employment contracts in the different type of jobs or whether they present different returns for the same characteristics. Most of the empirical studies that have investigated the permanent wage premium have looked exclusively at the conditional mean models and considered different ways of addressing the 2

4 selection issue related to contract type. I use the quantile regression technique to explore the source of heterogeneity in the wage gaps between temporary and permanent workers. Differently from the standard OLS approach, the quantile regression (hence after QR) framework provides a more flexible method to characterizing the effect of temporary status on different percentiles of the conditional wage distribution, thus enabling to shed further light on the location, scale and shape of the log wage distribution. Another advantage of QR model concerns the coefficient estimates that are more robust to outliers of dependent variable and, in presence of non-normal errors, may be more efficient than OLS estimates (Buchinsky, 1998). To examine the pay gap across wage profile, one has to go beyond the traditional OLS regression and Blinder-Oaxaca decomposition and to exploit several methods available to decompose the wage differential at each quantile. Thus I perform the Machado Mata techniques (hence after MM) for QR model to assess the relevance of glass ceiling or sticky floor hypothesis and to investigate the magnitude of difference in earnings between temporary and permanent workers. The MM techniques is applied using the procedure proposed by Melly (2006) to study the differences in distribution in the quantile regression framework. The empirical analysis decomposes the difference between the temporary and permanent log wage distributions into one component based on the difference in labour market characteristics (endowments effect) and one component based on the difference in rewards for the same characteristics (coefficient effect). The idea is to generate a counterfactual temporary log wage density that would arise if fixed-term workers were given permanent s labour market characteristics but continued to be paid like temporary. Nevertheless a possible source of misspecification may arise in this framework, the potential endogeneity of the temporary status which may bias the QR estimates, given that the role of unobservable individual characteristics cannot be ignored as well as the potential correlation between the temporary dummy variable and the error term in the wage equation. In order to address the issue of endogenous selection in temporary contract, this work examines the empirical implication of allowing the dummy variable for contract type to be correlated with the error term. Thus I adopt an IV method and a variant of the Heckman (1978) dummy endogenous variable model to correct the bias induced by the endogeneity of contract status. In particular for the IV approach I present a traditional 2SLAD estimator 1 and a Quantile Treatment Effect (QTE) estimation strategy (as Abadie et al., 2002) that allows to look at the impact of temporary status throughout the income distribution. 1 The 2SLAD estimator has been used in the literature about returns to schooling to correct the endogeneity of education level (see for example Arias et al. 2001; Girma and Kedir, 2005) but the fitted values approach may present some problem whether the treatment effect widely differs across quantile. 3

5 Differently the traditional self-selection issue, proposed by Heckman (1978) and present in the empirical studies on wage differentials, has been revised from Buchinsky (1998, 2001) in the QR framework, introducing a two-step in semi-parametric process to correct for the selfselection. In this paper I apply a variant of the Buchinsky approach to account for the selectivity bias in my wage equation. 2 The dataset used here to explore wage differentials is the 2006 wave of the Survey of Italian Households Income and Wealth (SHIW), a representative survey carried out by the Bank of Italy. Therefore I focus in my empirical exercise on the sub sample of employees with age between 15 and 65 years that are employed on temporary or permanent basis. In particular I wish to understand whether the temporary jobs evidence a wage penalty with respect to openend contracts and whether this gap is due to different individual characteristics or to discrimination in the labour market. Several studies have looked at the pay gap between temporary and permanent workers and in particular for the Italian labour market (Picchio, 2006, 2007; Tanda e Rossetti, 2007) they find the existence of a wage penalty for fixed-term jobs, lower with respect to other countries. But all these studies analyse pay gap at the conditional mean, which may hide significant differences at the bottom or top of the wage distribution. This study complements and adds to the previous research in many ways. Works on how much the temporary status wage penalty varies across the wage distribution have emerged recently and comparing wage not only at the mean is important to correctly capture the presence of segregation or discrimination and to evaluate the impact of individual characteristics at different point of earnings distribution. In addition I investigate more in depth the link between educational level and wage penalty that should be of great interest especially for policy makers for whom it is crucial to better understand the effects of flexibility in the Italian labour market. My study also complements Picchio (2006), which used the 2002 wave of SHIW to examine the wage differentials between temporary and permanent workers. Picchio (2006) looks at the wage penalty for temporary worker and accounts for self-selectivity bias in contract status dummy applying IV and sample selection models in a conditional mean framework. So this paper also contributes to the literature on the temporary-permanent wage differentials for the Italian labour market, controlling also for endogenous contract type in a QR framework. The main empirical findings are in favour of the sticky floor hypothesis, in the sense that the wage gap between temporary and permanent workers is wider at the bottom of the distribution, 2 The selectivity issue in wage gap literature has been widely account in several works. Previous studies has applied a variant of the traditional semi-parametric Bucinsky approach, exploiting several estimator (probit or other semiparametric model) to calculate the power expansion of inverse Mills ratio in the first step. Different example are Arulampalam et al. (2006) about union wage premia and Melly (2006) and Hyder and Reilly (2005) for public sector pay gap. 4

6 while at the top it is not significant. In particular the Machado-Mata decomposition shows how the coefficients effect (a measure of discrimination) is monotonically decreasing after the 30 th percentile, especially for women. Moreover the differences in the upper tail of distribution are explained by difference in labour market characteristics, as for example education, experience and occupation. The analysis by educational level and for sector confirms a significant negative coefficient effect for temporary workers in the lower tail of earnings distribution, which may indicate the port of entry nature of temporary employment, in particular for young and high-skilled workers. Finally correcting for endogenous self-selection in temporary contract modifies the magnitude of the differentials, without changing the main patterns, as QR regression. The plan for the paper is as follows. In section 2 I discuss the econometric model and the specification of quantile regression, as well as the decomposition method applied. Section 3 describes the dataset used for the empirical exercise, the rule for sample selection and presents some descriptive statistics. Section 4 reports the empirical findings and the decomposition of wage differential and finally section 5 draws the conclusions. 2) The econometric model 2.1) Quantile regression model In this section I disentangle the contribution of workers characteristics and contract type on wage setting process in the Italian labour market. Several contributions have examined the wage gap between temporary and permanent workers using a standard OLS framework 3 and taking a Mincerian standard specification 4 as starting point. It consists on estimating a traditional wage equation, including a dummy variable for temporary contract. To investigate whether the wage penalty (or premium) varies at different points of earnings profile, I deviate from this practice by looking at the effect of con tract type and other covariates on the whole wage distribution, thus employing a quantile regression model (Koenker and Basset, 1998). In addition, linear regression, as OLS and other standard statistical techniques, focus only on mean effect, emphasizing the impact of each covariate as a 3 For instance Picchio (2006, 20007), Tanda and Rossetti (2007) for Italy, Jahn (2008) for Germany, De La Rica (2004), Davia and Hernanz (2004) for Spain and Van Der Wiel (2008) for Netherlands. 4 The specification of the wage equation is an extension of well-known Mincer model of wage determination and it controls for age and its square, work experience (and its square), tenure in the present job (and its square), five education dummies, a dummy for contract type (temporary or permanent), region of residence, demographic characteristics (a marital status dummy and a dummy on whether one is the head of household, firm size dummies, industry dummies and three occupation dummies (white collar, blue collar and manager). Summary statistics are presented in table 1. 5

7 simple location shift (Melly, 2005). Therefore the quantile regression (QR) is a natural extension of OLS estimation of conditional mean model and it describes the conditional quantile regression as a linear function of observed heterogeneity, providing a detailed description of the conditional wage distribution. I specify the th ( 0 < 1) vector of covariates x i as < quantile of the log wage distribution ( w i ), conditional on a implying q ( w x ) = x i i i β w i = x i β + µ, with q ( µ x i ) = 0, th where µ is the error term of conditional quantile that is assumed to be zero. 5 Moreover QR results are robust to outliers and heavy tailed distributions. The quantile estimator of β solve the following minimization problem: ˆ β = arg min wi X iβ + ( 1 ) wi X iβ. β i: wi X iβ i: wi < Xiβ The minimization problem can be solved into a GMM framework which has been applied to demonstrate consistency and asymptotic normality of βˆ and to define its asymptotic covariance matrix. Thus, I estimate a single equation QR model as w i = α tempi + xiβ + µ where temp i is a dummy indicating contract type and equal to one whether the worker has a fixed-term job and zero if permanent. The set of QR coefficients provides the rates of return to the corresponding characteristics at the selected quantile of the conditional wage distribution. If the impact of temporary contracts is the same across the entire conditional wage distribution, I would expect α not vary for different. In addition, the variations in α across different quantiles could reflect heteroscedasticity. Moreover, if heteroscedasticity concerns interaction between temporary contract and unobserved determinants of wages, QR model allows to 5 This is the only distributional assumption on µ. QR model avoids the restrictive assumption that the error terms are identically distributed at all points of the conditional distribution. 6

8 derive how the fixed-term contract effect and unobserved heterogeneity impact on individual outcome across different quantiles. 6 Finally, the single equation model is based on the assumption that the wage determination process is identical for both permanent and temporary workers, i.e. the returns to individual characteristics are the same in both contract type. In order to test this restriction, I estimate a model interacting each independent variable with the contract type dummy and I investigate whether the interaction terms are significantly and jointly different from zero. The null hypothesis is rejected, thus the above mentioned assumption is violated. In practice the single equation QR model may be misleading and separate wage equation for each group are required. 2.2) Quantile regression decomposition Once I have estimated the QR coefficients, as in the OLS approach, the differences at selected quantiles of the wage distribution between two groups of workers can be decomposed into one component due to labour market characteristics and one component that is based on differences in rewards. In addition the implementation of quantile decomposition analysis may provide further evidence to understand whether the unobserved heterogeneity is a source in explaining the nature of the existent wage gap. 7 The usual Blinder-Oaxaca methodology is based on the OLS property that the mean wage conditional on the average characteristics of the sample is equal to the unconditional mean wage. Basically the exact decomposition of the average wage gap between both group of workers is due to the validity of this property. Hence incorporating the QR framework in this decomposition techniques based on conditional mean model may be misleading. th th Furthermore the unconditional quantile wage is equal to its quantile wage conditional on the vector of explanatory variables at the same quantile plus the average of those individuals error terms as q ( ). w i x i = x i β + µ But the error term in QR is not zero, so the exact decomposition of the wage differential (as in Blinder-Oaxaca methodology) cannot be performed at different quantiles. 6 In order to prove the heteroscedasticity hypothesis, i.e. the case in which slope coefficients are different for the same variables across quantile, I test that the estimated coefficients vectors from different QR are statistically different from one another. 7 In practice I investigate whether the existence of sticky floor or glass ceiling is due to the prevalence of a composition effect (differences in labour market characteristics, as educational level, experience, occupation) or a price effect (differences in rewards, i.e. whether the rate of return for the same characteristics is different). 7

9 More recently, Machado and Mata (2005) have proposed a quantile-based decomposition method, which combines quantile regression with bootstrap approach and it has been addressed in a wide range of empirical studies. 8 This procedure extends the traditional Blinder- Oaxaca decomposition on conditional mean wage to the whole wage distribution by allowing to overcome the above mentioned problem. Assuming linearity 9 between the quantiles of the dependent variable w i and the covariates X i, the main methodological contribution of the Machado-Mata (MM) procedure is to derive an estimator of counterfactual unconditional wage distribution. In this paper I follow Melly (2006) who suggests a modified procedure of MM technique to decompose differences at different quantiles of the unconditional distribution. Instead of randomly drawing from an uniform U (0,1), the conditional distribution is estimated by quantile regression for a large number of selected s, such that 1,.., j,.., J (with j = 1,, J) and then the conditional (log) wage distribution is integrated over the range of the explanatory variables. Let ˆ β = ( ˆ β,..., ˆ β,..., ˆ β ) be the QR coefficients estimated at J different j 1 J quantiles, 0 < 1 (with j= 1,, J) separately for both temporary and permanent workers. < J Then, integrating over all observations and over all quantiles, Melly (2006) derives an estimator of the th unconditional quantile of (log) wage as follows N J 1 q( X i, β = q j j x ˆ, ) inf : ( 1 )1( iβ q) j N i= 1 j= 1 where 1( ) is the indicator function. In what follows, using the above estimator for unconditional distribution, Melly (2006) estimates the counterfactual distribution by replacing either the estimated parameters of the distribution of characteristics of permanent workers with those of temporary workers. In addition the difference at each quantile of the unconditional distribution can be separate into one component that calculates the difference in the rewards that the two groups (temporary and permanent workers) receive for their labour market characteristics (coefficients effect) and one 8 Other decomposition procedures have been provided in the literature in order to disentangle the sources of differences in wage distribution. For instance, the plug-in methods of Juhn et al. (1993), based on parametric regression, or Di Nardo et al. (1996), that exploit sample reweighting to apply a semi parametric model. However numerous empirical studies have mainly focused on the Machado-Mata technique to decompose differences along the whole wage distribution, exploiting quantile regression framework. 9 th This means that the conditional quantile is correctly specified as q ( w i x i ) = x i β (0,1). 8

10 component that is based on differences in labour market characteristics between temporary and permanent workers (characteristics effect): t t p p q(, β, )- q(, β, ) = x i x i [ q ( x t t, β ) q ( x t p, β )] + [ q ( x t p, β ) q ( x p p, β )] where t = temporary, p = permanent, the first brackets measure the difference in the rewards that the two groups receive for their labour market characteristics, exploiting the counterfactual distribution, while the second brackets measure the impact of differences in labour market characteristics between fixed-term and permanent workers. 10 Overall, the Melly (2006) decomposition generalizes the traditional Blinder-Oaxaca approach and illustrates how differences in rewards or in labour market characteristics affect the wage gap between the two groups across the entire distribution. However an important disadvantage of this methodology is that, unlike the classic Blinder-Oaxaca, it cannot be used to separate the contribution of each variable, thus I can report only the total endowment and coefficients effect for each selected quantile. 2.3) The Endogeneity issue in contract type As widely discussed in the literature, standard QR results may be biased due to the endogeneity of contract type. In practice, if the choice of working under a temporary or a permanent contract is not exogenous and the workers do not have the same probability of being hired under each type of contract, a self-selection bias may arise due to the non random distribution of employment contracts. Indeed the role of workers unobserved characteristics on both wages and contract type selection cannot be ignored and accounting for endogenous selection may be necessary to correct the bias mentioned above. A further potential source of misspecification derives from a sample selection problem. The information on wages is only observable for wage earners, i.e. for those individuals who decide to participate to the labour market. Moreover, being a wage earner may be a characteristic distributed not randomly across the population and whether the error term of the labour market participation model is correlated with the error term of the wage equation, the QR may yield biased estimates even if the endogeneity of contract type is controlled for, due to a sample selection distortion. 10 For a more detail description of this decomposition approach see Melly (2006). I use Stata package rqdeco (Melly, 2007), estimating 100 quantile regressions in the first step and then to obtain consistent standard errors I bootstrap the results with 100 replications. 9

11 Therefore, to account for the potential endogenous selection in temporary contract, I replicate the analysis, exploiting an IV approach and a self-selection model, and in the next two section I will describe the estimation strategy used to deal with endogeneity issue ) An extension of IV: the Quantile Treatment Effect Several studies on wage differentials have dealt with the possible non-random selection in temporary contracts and have used different estimation strategy in order to account for the endogeneity bias. In particular an IV approach has been adopted to correct for the endogenous self-selection in the literature for the Italian labour, using different excluded instruments. For instance, as instrument, Tanda and Rossetti (2007) use information on whether the workers enters in the labour market after the Treu reform (so being potentially exposed to temporary contracts) or not, exploiting the timing of change in labour market regulation. Further, Picchio (2006) estimates different IV specifications, using an instruments on the job searching dummy variable and whether the worker has taken sick days or not. 11 In addition, the issue of endogenous variable is not straightforward in the quantile regression framework and thus to address the self-selection bias, differently by previous literature, I adopt an instrumental variable quantile regression (IVQR) approach that looks at the quantile treatment effect (QTE) of being a temporary worker on wages. Moreover, to perform the QTE estimator, I decide to follow Picchio (2006) and, as instrument, in this paper I use the on the job searching dummy variable, which is equal to one whether the employee is looking for another work or zero otherwise. The consistency of IV estimator is based on the correlation between the instrument and the endogenous dummy variable (being a temporary worker) and on its exogeneity. The searching dummy variable is supposed to be positively correlated to the contract type indicator, because temporary workers should have a higher incentive to search, giving their higher probability to be laid off at the end of the contract. Furthermore the first stage of a 2SLS estimator confirms that the on the job searching and fixed-term contract are positively correlated, with a positive estimated coefficient, statistically different from zero In this case the author provides both an IV and a GMM specifications in the study of wage differentials between temporary and permanent workers. GMM estimation strategy allows to test for the jointly validity of the instruments with the Hansen Sargan test of over identification, so providing a robustness check on endogeneity of contract type. Moreover, he also discusses the possibility to include, as instrument, information on whether the employee has never paid social security contributions. 12 An issue much debated in the IV framework is the weakness of the instruments used in the empirical analysis, as discussed in Staiger and Stock (1997). For instance, in this specific case, with one endogenous variable and one excluded instrument, the model fall into the just identified case and thus the validity of the instrument cannot be test. 10

12 The extension of instrumental variable methods to the estimation of conditional quantile model is discussed firstly in Amemiya (1982). 13 In practice, the estimation strategy consists in using the fitted values from a first step least squares regression of the endogenous variable on the instruments as covariate in the standard quantile regression at the second step. In literature this model is the so-called fitted value approach (2LAD). But, applying a 2LAD estimator, analogous to a 2SLS one, it will most likely result into biased and underestimated standard errors. Thus, to recover consistent standard errors, an approach may be to bootstrap them in both the first stage and in the second stage regressions. 14 Based on the above model and for a comparison device, in this paper I estimate a 2LAD model where the first stage is a regression of the endogenous variable (temporary contract) on the exogenous ones (including the instrument) with a probit model, while the second stage is a linear quantile regression with the fitted value for temporary status. 15 However, as suggested in previous studies, the fitted value approach is not consistent whether the treatment effect differs across quantile. Other alternative approaches of IVQR estimator have been discussed in the literature (for a detailed description see Frolich and Melly, 2008; Melly, 2006). The subject of quantile regression with endogenous variables has been investigated by Chernozhukov and Hansen (2005) who provide a model of IVQR in presence of discrete endogenous variable. But, as discussed in the introduction, I adopt a quantile treatment effect (QTE) model, following Abadie, Angrist and Imbens (2002) approach, that allows to look at the impact of contract type throughout the wage distribution, controlling for endogenous self-selection in temporary contract. The comparison of both models shows that Abadie et al. (2002) impose more restrictive conditions on the selection equation but allow for heterogeneity in responses. 16 Therefore I exploit the peculiar feature of QTE approach in order to emphasize the heterogeneous impact of flexible contracts across the wage profile. Alternatively, as suggested by Picchio (2006), on the job searching could have a direct effect on wages whether, for example, the employer decides to offer an higher wage to avoid that the worker accepts another job. Therefore, in this case, the IV estimator is not consistent. In order to make the Quantile Treatment Effect (QTE) approach more robust, I have also run a further specification in which the instrument used is the dummy variable sick, equal to one if the employee has taken days for sick and zero otherwise, as proved in Picchio (2006). The results are quite similar and the main patterns do not change. Finally, to overcome the possible weakness of the instrument, one could use the lagged incidence of temporary employment by region, skill and sector to control for local availability of temporary job by skill and sector. But, to exploit the QTE estimator proposed by Abadie et al. (2002), I haveto use a binary instrument and so the on the job searching seem to be a quite robust choice. 13 Amemiya (1982) has considered quantile regression model combined with an endogenous variable, reporting the consistency and asymptotic normality of a 2LAD estimator, but having in mind a conditional median regression (LAD model) 14 Arias et al. (2001) use the bootstrap approach to obtain consistent standard errors when they investigate return to schooling with instrumental variable quantile regression. A similar framework is udes by Garcia et al. (2001) in a study on gender wage gap applying QR model. 15 Both stage are calculated using the bootstrap technique with 100 replications. 16 I mean heterogeneity conditional on X and the quantile of interest, while both estimators allow for different treatment effects at different quantiles (see also Melly, 2006) 11

13 Abadie et al. (2002) propose a parametric estimator, based on the local average treatment effect (LATE) model of Imbens and Angrist (1994), which can be applied only to a specific case: a binary endogenous treatment variable D and a binary instrument Z. Abadie et al. (2002) provide conditions under which a Quantile Treatment Effect (QTE) model can be estimated: 1. Independence assumption, i.e. ( 1, Y0, D1, D0 ) 2. Non trivial assignment, 0 < P ( Z = 1 X ) < 1 3. E [ D1 X ] E[ D0 X ] 4. Monotonicity assumption, i.e. P ( D1 D0 X ) = 1 Thus for each ( 0 < < 1) there exist δ and Y is jointly independent of Z given X. β such that ' ( Y X, D, D1 D0 ) = δ D X β q > +, where q ( Y X, D, D 1 > D0 ) denote the -quantile of Y given X and D for compliers. Under these conditions, I can compute a consistent estimator of δ and The four conditions described above are derived from Angrist and Imbens (1994) in order to recover the local average treatment effect (LATE) interpretation of 2SLS. 17 Under these assumptions, Abadie et al. (2002) identify the marginal distribution of the potential outcomes for the sub-population of compliers and they suggest that the conditional quantile treatment effect can be estimated as a weighted quantile regression: β. ˆ ˆ AAI ( β, δ ) = arg min, W. ρ ( Y X β Dδ ) IV IV β δ i τ i i i where W AAI i Di (1 Z i ) (1 Di ) Z i = Pr( Z = 1 X ) Pr( Z = 1 X ) i i More generally, the QTE approach captures the impact of an intervention on the whole distribution for individuals whose treatment status is changed by a binary instrument In this framework, the first assumption implies that searching for another job is randomly assigned. In practice I cannot test this assumption, but I find that temporary workers are not significantly different from each other whether they search for another job or not. The third condition simply requires a significant first stage, as I explained in this section. The fourth condition basically implies that there not exists workers for whom searching another job reduces the probability to be temporary. In addition the model requires the presence of compliers and the treatments effects can be identified only for this group. 18 A preliminary estimator for Pr( z = 1 x ) i is necessary to implement QTE approach, but some of the weights may be negative. Moreover, Abadie et al. (2002) use a series estimator, while the Stata package IVQTE used in the estimation procedure, applies a local estimator, setting to zero the estimated weight that are negative in finite samples. 19 Finally, I exploit bootstrap technique with 100 replication in order to obtain robust standard errors. 12

14 2.3.2) Self-selection approach: an extension of Dummy Endogenous Variable Model To guarantee the robustness of QR estimates, I need to account for a potential self-selection bias. Indeed if I do not correct for endogenous selection, usual QR risks yielding biased estimates, given that the disturbance term and the independent variables in the wage equation could be correlated. Either through a self-selection by workers or sample selection by employers, the location of individuals in either contract type may not be considered as the result of a random process. For the QR model, I control for endogenous selection by applying a variant of the standard Heckman two-step procedure (1978), as it was introduced by Buchinsky (1998, 2001) and based on a non parametric method. There is currently little consensus regarding the most appropriate correction procedure for selectivity bias in QR model, also exploiting a higher order series expansion, based on the inverse Mills ratio. Nevertheless this approach presents some complications that arise in regard to identifying the constant term in such wage regression models when higher order terms are used to capture selection bias. To get unbiased estimates of β, it is necessary to introduce an extra term in the quantile wage equation to correct for selectivity as evidenced: where q ( w i ' x = x ) = x β + h ( g) + ε i h ( g) q ( u x, g > 0) i i such that q ( x, g > 0) = 0 ε i i. Following the two-step Buchinsky approach, the h (g) is approximated by a power series whose coefficients has to be estimated and should define a function which is larger when the impact of unobservable is larger. This function is the inverse Mill s ratio, being small for those with an high probability of being temporary and increasing monotonically as the probability of being temporary reduces. As exclusion variable in the first step, I adopt on the job searching dummy variable. 20 Hence I control for the selectivity bias in QR wage equation expanding h (g) as a power series in the inverse Mill s ratio. In the first step I have to estimate the probability of workers being in temporary or permanent contract. The traditional method in the selection step uses a semi-parametric least square which 20 Whether I suppose that there not exist exogenous variables which account for the selection into temporary contracts and which are excluded from the wage equation, the identification of the self-selection model derive from a distributional assumption, i.e. the non linearity of the correction term (hazard term). 13

15 makes no assumptions about the distribution of the residuals. However a different strategy is followed in this paper, where I apply two ordinary probit selection equations (distinguishing by region, i.e. North vs. Centre-South) similarly to Heckman (1979) and from there derive the bias correcting factor (i.e. the inverse Mill s ratio), as in Arumpalam et al. (2006). In the second step, a linear quantile regression is performed by additionally including the derived correcting factor. The h (g) function is approximated by the inverse Mill s ratio and its square. A different model specification with a series of power 3 (of Mill s ratio) is tested and the result is similar. 3) Dataset and descriptive statistics The empirical analysis has been carried out also on the 2006 wave of the Survey of Italian Households Income and Wealth (Shiw), a nationally representative survey conducted every two years since 1989 from the Bank of Italy. It covers 7,768 households composed of 19,951 individuals and 13,009 income-earners, providing information about individual and job characteristics, contract type (temporary, interim and permanent work), the average monthly wage and the hour worked. The 2006 wave of SHIW dataset covers 7,236 employed workers of which 5,808 employees and 1,424 self-employed workers. To investigate the impact of temporary contracts on wages, I select the sub-sample of employed workers but removing the self-employed worker since their earnings are driven from more complex factors, as taxation, and they are structurally different from employees. Then I excluded observation lying in the first and in the last percentiles of the weekly working hours and yearly earnings respectively. Further I consider only individual with a working age between 15 and 65 years, excluding observations which have missing values for some covariates. The main variable is the type of contract temp i, a dummy variable equal to one whether the individual is fixed-term or interim worker and equal to 0 if the individual has an open-end contract. The dependent variable is the logarithm of the average hourly wage, defined combining the information provided by the SHIW on the yearly earnings and average working hours. In particular employees are asked to specify how many months they are worked during the year and in the same way the average weekly working hours including overtime. Differently fringe benefits are removed from total earned income, which is net of taxes and social security contribution. Exploiting this information I can compute the logarithm of net hourly wage for all employees in the sample, both temporary and permanent. 14

16 In order to draw a picture of temporary work and wage gap in Italy, I present some descriptive statistics, computed using the 2006 wave of SHIW. Table 1 shows the profile of employees, distinguishing then between temporary and permanent workers. Employment, permanent one in particular, follows a stronger gender pattern. Further the level of education is higher on average for permanent workers with more than 51% that have at least an high school qualification while for temporary the same percentage is around 47%. Regarding the age profile, fixed-term jobs are diffused among the youths, with more than 70% of temporary workers having less than 40 years. Differently the open-end works are concentrated among the adults where more than 50% is older than 40 years. This clearly illustrates the strategy of flexibility at the margin, with an higher diffusion of temporality rate among the weaker categories, as young workers, women and immigrants. From a macro-region analysis, table 1 reveals how in the Southern there are the 44% of temporary workers, while only 24% of permanent ones, so confirming the dual structure of Italian labour market. Moreover the 55% of permanent workers are resident in the North. Then the distribution of workers among occupations is related to one of the skill levels: high qualified worker (manager) and white collar tend to register lower temporality than unskilled workers and blue collars. And last but not least fixed-term employment is quite unequally spread across sectors and different firm size. Thus it common in building and in agriculture and it is likewise used by small and medium firm up to 50 employees. On the opposite extreme public services and industry and mining are the ones that register the highest portion of permanent position, together with large firm, higher than 50 employees. Table 2 displays a picture of the unconditional wage dispersion for temporary and permanent workers at various percentiles of the distribution (10 th, 25 th, 50 th, 75 th, 90 th and median). I also show a measure of the wage dispersion, the spread for both contractual status. The unconditional log hourly wage evidences a wider gap at the bottom of distribution, which decreases as I consider the upper tail of distribution. Moreover the spread is higher for temporary than for permanent workers. Hence the data suggests the presence of a glass floor hypothesis, exhibiting a stronger wage differential between temporary and permanent at the lower percentile of distribution. The figure 1a and 1b provide a visual summary of the temporary and permanent wage distribution and the density functions were estimated using an Epanechinov kernel estimator. It can be seen from these figures that the distributions are quite distinct between contractual types. The permanent earnings distribution is characterized by a higher density function around the mode and a lower dispersion with respect to temporary distribution. But to control for the 15

17 effects of differences in the distribution of worker characteristics between contract type, I look at the quantile regression model in the next section. 4) The empirical results Labour market literature on wage differentials has recently discovered the importance of controlling for the difference in pay gap along the whole distributions, given that wide differentials may arise at the bottom or at the top of distribution (for example see Melly, 2006; Arulampalam et al. 2006). In the quantile regression analysis two main effects may be identified. A glass ceiling effect is identified, in this study, when temporary workers, who are otherwise similar to permanent ones, tend to fall behind permanent at the top of wage distribution, while a sticky floors phenomenon is identified when the gap between temporary and permanent workers widens at the bottom of distribution. In the next paragraphs I present the quantile estimates with and without sample selection and the wage gap decomposition, applying the Machado-Mata techniques. 4.1.) Quantile regression In this section I present the results for the econometric model outlined in section 3 to investigate whether the relationship between hourly wage and individual characteristics differ between temporary and permanent workers along the different quantiles of the whole wage distribution. According to the descriptive statistics presented in table 1-3, the discrepancy between the permanent and temporary log wage could be in part derived from differences in permanent s and temporary s labour market characteristics as for example age, education, occupation and industry. Thus in table 4 I further investigate the wage gap evolution between permanent and temporary workers throughout the wage distribution and I present the quantile regression respectively for the 10 th, 25 th, 50 th, 75 th and 90 th quantile, controlling for individual and firms characteristics. Due to limited number of temporary in my sample, I believe that the comparison could be flawed at the bottom or at the top of the wage distribution. Furthermore the coefficient of contractual type dummy may be considered as a measure of the impact of temporary status on the wage profile for each worker, a sort of raw index of labour market discrimination against temporary workers. My results are in favour of the sticky floor hypothesis for atypical workers, in the sense that the wage gap is wider at the bottom of the distribution, as evidenced in table 4. 16

18 At the bottom of the distribution (10 th percentile), the gap is about 20,6% and it is statistically significant at the 1%. Then the temporary-permanent wage differentials is lower at the 25 th and 50 th percentile, around 13,3% and 11,3% and always statistically significant at the 1%. A further reduction is present at the 75 th percentile where the gap is now slightly more than 6% and significant at the conventional level. Finally the data shows a marked reduction in the wage differentials at the upper tail of distribution (90 th percentile) where the sign is reverse and the coefficient is now positive, around 3,3% but not statistically significant. These results reject the hypothesis of glass ceiling which prevents temporary from reaching high wages, suggesting that the link between flexibility and wage gap could be a problem for weaker workers at the bottom of the distribution. Figure 2 reports the coefficient estimates and their 95 per cent confidence intervals for the temporary dummy, comparing quantile regression and OLS models by gender. 21 Comparing the estimates from quantile and OLS regression, it notes that for both females and males the OLS coefficient tends to underestimate the wage penalty for temporary workers until the 60 th percentile. In particular the difference between OLS and quantile estimates appear more wider at the bottom and top ends of the conditional wage distribution both for male and female workers. To confirm this feature and to shed further light on the nature of wage gap, I look at the effect of explanatory variables on log hourly wage across the whole distribution, to find a theoretical explanation to the glass floor hypothesis. As I carry out different quantile regression on the combined temporary and permanent dataset, the temp dummy coefficient can be simply interpreted as a measure of the extent to which wage gap between the two groups of workers remains unexplained at each quantiles after controlling for individual and job characteristics. The effect of age is not clear cut across various quantiles, with a positive value around 1% at the 25 th percentile and statistically significant at 10% and the opposite sign at the 75 th percentiles, while for other percentiles the coefficient is not statistically significant. Differently the impact of experience is increasing and slightly positive in column 1-4, but stronger at the top of the distribution and characterized by decreasing marginal rate of return, given the negative sign on experience squared. A similar but less marked picture is for tenure. Looking at the education and taking the elementary or none as base category, in column (1) I observe a positive and statistically significant for all four coefficient, with a larger value for university degree, around 23% that in column (5) at the 90 th percentiles is more than double, 21 These graph are obtained using Stata and the grqreg module due to Azevedo (2004) that graphs the coefficients from quantile regression and the standard errors are calculated via bootstrapping with 50 replications. Further it graphs the coefficient and confidence interval from an OLS regression on the same model. For quantile regression the estimates are calculated at each 0,01 percentile point, as well as for the confidence intervals. The OLS estimates are represented through the horizontal line and specific upper and lower 95% confidence interval in the figure 2. 17

19 47,7% and always statistically significant at 1%. A similar but lower trend is for other level of education in the different percentiles examined. The analysis for macro-regions reveals some interesting patterns: considering the North-East as reference category, at the bottom of distribution to stay in the North-West and in the Centre has a slightly negative effect on log hourly wage. Differently to live in Southern has a stronger negative impact. The estimates for the 25 th percentile report a penalty around 3% for the North-West and 14% for the South, both statistically significant at 1%. The pattern changes at the top of distribution, in particular looking at the 75 th percentile the difference between the North-West and the South is now narrower, probably because for the high-wage jobs the penalty of living in the South is lower. In addition, the firm size dummy variables show an increasing wage rate with the number of employees that is stronger at the bottom than at the top of wage distribution. For example to be employed in a firm with more than 500 employees increases the wage of 24% at the 10 th percentile and of 19% at the 90 th percentile, using always as reference category firm up to 4 employees. The effects are all statistically significant at the conventional level. Furthermore the public firms positively affect the wage in particular at the bottom of distribution, as shown in column (1) at 10 th percentile, with an effect around 28% and statistically significant. This impact tends to be lower at the top of the distribution, as for example in column (5) at the 90 th percentile (around 19%). A possible explanation is that public sector has a more compressed wage distribution and the public sector wage premium could be highest at the lower end of the wage distribution and then to decrease monotonically, as found for other countries. A reverse pattern is shown whether I look at the manager dummy which effect is instead monotonically increasing along the whole distribution with a larger spread from the 10 th to the 90 th percentile (18% vs. 27%). At last the gender dummy seem to indicate the presence of a constant gap between male and female around 9-10%, always significant and similar in almost percentiles estimates. To exploit the gender differences, I replicate the model for both male and female and in table 5 and 6, I report the quantile regression for men and female separately. Table 5 shows the estimates for female, exhibiting the same pattern as the above model for all sample, but some important dissimilarities between female and male appears, for instance in the magnitude of coefficients. As mentioned previously, the temporary status has a lower negative impact for female workers. Indeed at the 10 th the gap is around 14% and statistically significant at 1% and this pattern is confirmed until 50 th percentile where the coefficient is (about 8%), so accepting the glass floor hypothesis. But these estimates evidence how the penalty for temporary status has also a gender dimension that favours female. Nevertheless 18